I don’t believe “Mind” is what Catholics believe God’s being to be. God’s essence is Love. Whether essence corresponds to being, I’m not sure. However, “person” includes intellect and will.
Perhaps expand on what you mean by “Mind.” I would think intellect and will are something like constituent parts of a conscious mind, but if that’s true, then there would be three minds in God, not one, corresponding to each person.
That’s how I would think about it, which is why I associated your idea with schizophrenia. But, as I said, let’s explore what you mean by “mind,” and maybe we can work more clearly from there.